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always better to get a second set of rims...works out cheaper and better for the tires long run with the constant swapping on and off rims twice a year. and the time you spend waiting for the tires to be remounted and balanced each time.

tire rack sometimes has some great deals when they try to clear inventory.

rims - i'm partial to OEM even for winters. try kijiji? Not sure if the offset of the rims are different from the e60 generation. many used sets of rims from that MY. if they work get those. knock offs sometimes vary in quality and a cracked rim in the winter is far more troublesome than in summer. and we know how pot hole ridden the city becomes in the winter.

Buy a canadiantire patch kit, can of tire inflate, and a portable pump and you are good.
I've had to use it once, and never missed not having a spare tire (nor run flats).
..... didn't even remove the tire.

TireRack has a Firestone Winterforce 17" on Alloys for $992/set
I'd run a 225/55/17 for snows (all four - thinner is better)

You culd run 245/50/17 on the bigger 5 Series.

You could also run 225/50/18 tires.

I usually don't install the TPMS either for the winter setup ..........Your call.

^ that's what i did...bought a used set that way and used the tires for 2 more seasons before selling them. there's always people looking to put tires on with just a bit more tread to pass safety when they do a lease return.

and yes go for smaller size tire for winters. the door jamb and manual will show the proper M+S sized tire.

and as others have stated avoid the dealer purchase. really you don't need star rated tires.

it is good to run a narrower tire for winter that has the same overall "turns per mile" as the stock tire. Tire rack is a great resource with their online fitment or by phone. I have been really happy running Pirelli Carving or Winter210.